Question: $f(x)=2x^3+8$ $h(x)=\sqrt[3]{12-5x}$ Write $(f\circ h)(x)$ as an expression in terms of $x$. $(f\circ h)(x)=$
First, let's write $(f\circ h)(x)$ as $f(h(x))$. Next, we write $h(x)$ as the input to function $f$. $f({h(x)})=2({{h(x)}})^3+8$ Since $h(x)=\sqrt[3]{12-5x}$, this becomes: $\begin{aligned} f({h(x)})&=2({\sqrt[3]{12-5x}})^3+8\\ \\ &=2(12-5x)+8\\ \\ &=24-10x+8\\ \\ &=32-10x \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(f\circ h)(x)=32-10x$